Related papers: Multiple solutions for the equilibrium populations…
In previous mathematical studies of the BCS gap equation of superconductivity, the gap function was regarded as an element of a space consisting of functions of the wave vector only. But we regard it as an element of a Banach space…
Based on weakly-coupled anisotropic BCS theory, the dependence of energy gap and specific heat on temperature are evaluated for superconductor MgB$_2$, and the results are compared with experimental data.We show that the weak coupling…
This review is written at the time of the twentieth anniversary of the discovery of high temperature superconductors, which, nearly coincides with the important discovery of the superfluid phases of ultracold trapped fermionic atoms. We…
In conventional superconductors, the pairing energy gap (\Delta) and superconducting phase coherence go hand-in-hand. As the temperature is lowered, both the energy gap and phase coherence appear at the transition temperature T_c. In…
Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized BCS gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this…
In the preceding work \cite{watanabe3}, it is shown that the solution to the BCS gap equation for superconductivity is continuous with respect to both the temperature and the energy under the restriction that the temperature is very small.…
An analysis of the different approaches used within the van Hove BCS model for the high temperature superconductors has been done. How far the employment of an asymptotic expression for the density of states underestimates the thermodynamic…
We show the temperature dependence such as smoothness and monotone decreasingness with respect to the temperature of the solution to the BCS-Bogoliubov gap equation for superconductivity. Here the temperature belongs to the closed interval…
We present a numerically exact solution for the BCS Hamiltonian at any temperature, including the degrees of freedom associated with classical phase, as well as amplitude, fluctuations via a Monte Carlo (MC) integration. This allows for an…
We deal with the gap function and the thermodynamical potential in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature $T$ only. We show that the squared gap function is of class $C^2$ on…
The solutions of a renormalized BCS equation are studied in three space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model…
In the [BCS] paper the theory of superconductivity was developed for the BCS model, in which the (instantaneous) interaction is only between fermions of opposite momentum and spin. Such model was analyzed by variational methods, finding…
In part I of this paper a modified BCS mechanism of Cooper pair formation of electrons was proposed. This mechanism is connected with the existence of a narrow, roughly half-filled "superconducting energy band" of given symmetry. The…
A brief introduction is given in the generic microscopic framework of superconductivity. The consequences for the temperature dependence of the kinetic energy, and the correlation energy are discussed for two cases: The BCS scenario and the…
Strong evidence for pairing and superfluidity has recently been found in atomic Fermi gases at the BCS-BEC crossover both in collective modes and RF excitation energies. It is argued that the scale for the effective pairing gaps measured in…
We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but includes also direct and exchange energies. We show that for…
An integrating theoretical scenario of superconductivity and superfluidity has been built. It reduces to the special BCS superconductivity mechanism for conventional superconductor and to a new theory for high transition temperature…
We present a detailed study of the BCS pairing transition in a trapped polarized dipolar Fermi gas. In the case of a shallow nearly spherical trap, we find the decrease of the transition temperature as a function of the trap aspect ratio…
A General Theory of Superconductivity with points of view differing from those of the BCS Theory is presented in two parts. In the first part, a general equation for the superconductivity is obtained; based on the stable pairing of two…
The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature and the critical temperature. This study bridges two regimes where quantum and thermal fluctuations are, respectively, important. The…